基于正则化理论的地应力场反演及其工程应用

In-Situ Stress Field Inversion Based on Regularization Theory and Its Applications

为了提高地应力场反演算法对观测误差的鲁棒性,提出了基于Tikhonov正则化理论的地应力场回归系数反演算法。研究表明,随着正则化因子的增加,最小二乘法法方程系数矩阵的条件数会逐渐减小,但目标函数却在逐渐增加,拟合精度也会逐步降低。为了提高反演模型的预测精度,提出了一种构造应力随埋深线性变化的假设模型。工程实际应用结果表明,与传统的矩形构造应力模型相对比,改进反演模型预测地应力的最大误差由10.96%变为1.93%,验证了所提出改进反演模型的精确性。考虑观测噪声的影响,数值模拟结果表明,所提出的地应力回归系数反演算法具有良好的鲁棒性。

In order to improve the robustness of inversion algorithm of in-situ stress field to observation error,an inversion algorithm of in-situ stress field regression coefficient based on Tikhonov regularization theory is proposed.The research show that:With the increase of regularization factor,the condition number of the coefficient matrix of the least squares equation would gradually decrease,but the objective function was gradually increasing and the fitting accuracy would gradually decrease.In order to improve the prediction accuracy of the inversion model,a hypothetical model of linear variation of tectonic stress with buried depth was proposed.The engineering application results showed that compared with the traditional model of rectangular tectonic stress,the maximum prediction error of the improved inversion model in predicting in-situ stress was reduced from 10.96%to 1.93%,which verified the accuracy of the proposed improved inversion model.The proposed inversion algorithm of in-situ stress regression coefficients has good robustness.